Prandtl-Meyer expansion of an ionizing monatomic gas

The Prandtl-Meyer flow of a pure, monatomic gas, including the effects of ionization and recombination, has been numerically calculated. Expressions describing the thermodynamic state of the gas mixture were obtained from statistical mechanics, the components making up the mixture being considered as perfect gases. Expressions describing the kinetic behavior of the ionizing-recombining gas mixture, using J. J. Thomson's three-body recombination coefficient, and expressions describing the gas dynamic behavior of the reacting gas mixture were derived. An iterative method of solving the equations governing equilibrium flow was derived. Solution was carried out, using an IBM 1620 Data Processing System, for a particular initial state: degree of ionization = .9000, dimensionless temperature = .1250 (=35,650°K in Helium), Mach number = 1.000. Curves showing the variation of the state and motion variables obtained are presented. Using the assumptions that the pressure distribution along a streamline and the shape of a streamline in a non-equilibrium Prandtl-Meyer flow are the same as for an equilibrium flow with the same initial conditions, the governing flow equations were reduced to two, coupled, ordinary differential equations in the degree-of-ionization and velocity distributions along a streamline. Solution of these equations, using the pressure distribution and streamline shape obtained from the corresponding equilibrium flow, gives the degree of ionization and velocity along a particular streamline as functions of angular position in the expansion wave. Numerical solution of these equations, using an IBM 1620 Data Processing System, was carried out for flow from an initial state the same as the above equilibrium solution, along six streamlines ranging from very near to the corner (.086 cm in Helium) to very far from the corner (86 cm in Helium). Curves showing the variations of the state and motion variables obtained are presented